In a system that includes a physical forwarding element (PFE), the mapping of each possible destination MAC address to a destination port number of the PFE is stored in a mapping table. A destination port number on the PFE is identified for a first packet in a sequence of packets arrived at a source port of the PFE by searching the mapping table and stores the destination port number in a caching table. For each packet after the first packet, when the destination MAC address of the packet matches the destination MAC address stored in the caching table, the destination port number stored in the caching table is used as the destination port number of the packet. Otherwise, a destination port number for the packet is identified by searching the mapping table and the destination port number stored in the caching table is replaced with the identified destination port number.